This invention relates to fluid dynamic force development on moving and nonmoving fluid dynamic structures. The most common fluid dynamic structures to use this invention are airfoils such as wings and propellers and water based lifting and drag structures.
The patents listed below constitute a representative listing of the prior art in this field:
Pat. No.Issue DateInventor994,968Jun. 13, 1911Barbaudy1,050,222Jan. 14, 1913McIntosh1,841,921Jan. 19, 1932Spiegel1,939,682Dec. 19, 1933Fleming2,576,981Dec. 4, 1951Vogt2,775,419Dec. 25, 1956Hlobil2,805,830Sep. 10, 1957Zborowski3,270,988Sep. 6, 1966Cone4,050,397Sep. 27, 1977Vanderleest4,146,199Mar. 27, 1979Wenzel4,714,215Dec. 22, 1987Jupp et al.5,102,068Apr. 7, 1992Gratzer5,348,253Sep. 20, 1994Gratzer6,474,604Nov. 5, 2002Carlow
The drag on any fluid dynamic structure occurs due to shape, compressibility, and lift. At speeds below the critical Mach number, drag due to lift is a major factor for any vehicle moving in a fluid. When a wing or a foil moving or immersed in a flowing fluid generates a normal force (lift), the surface facing the direction of the lift force is at a lower pressure and the surface in the opposite direction from the lift force is at a higher pressure. The fluid at the higher pressure moves toward the lower pressure. At the trailing edge of the wing or foil, this pressure differential resolves itself in the wake of the aerodynamic structure and aids in force production. At the unbounded edges of the wing or foil (wingtip or unconnected foil end) the high pressure moves spanwise (normal to the fluid flow and parallel to the wing or foil) and produces a helix-shaped vortex with a centerline parallel to the tangent of the wingtip and the far field fluid flow. The loss of pressure from the high pressure surface and the increase in pressure on the low pressure surface results in decreased lift. The vortex wake results in induced drag proportional to the lift on the wing or foil and defined by:
      Drag    induced    =            1      2        ·    ρ    ·          V      inf      2        ·    S    ·                  C        L        2                    π        ·        k        ·        AR            
where
ρ is the density of the fluid
Vinf is the freestream velocity of the fluid or wing/foil
S is the area of the wing/foil
CL is the lift coefficient of the wing/foil
k is the span efficiency factor of the wing/foil
AR is the aspect ratio (b2/S) of the wing/foil and b is the span
The span efficiency factor, k, depends on the spanwise load distribution and the configuration of the lifting system. For a planar wing/foil, an elliptic loading is optimum and k=1.0. As can be seen in the equation, increasing the aspect ratio and/or the span efficiency factor of the wing/foil will reduce the induced drag. Aspect ratio is directly related to wing span and chord. Various means have been proposed to increase the apparent (mathematical) aspect ratio and apparent (mathematical) span efficiency factor through the use of tip winglets or end-plates, multiwing configurations of various types, and various forms of arched lifting surfaces either opened or closed. All of these mechanisms endeavor to increase the mathematical aspect ratio and mathematical span efficient factor without actually adding wing span, decreasing chord length, or making the wing more elliptical. Assorted tip devices involving the use of multiple surfaces have been proposed for application to wings and foils. Many of the above are not particularly efficient or useful for various reasons including excessive structural weight, high loads, concomitant drag sources, and operational limitations. Therefore, with the exception of the monoplane with winglets, they find little use today. Several forms of winglets are currently in use for applications where span and operational space may be limited or where existing aircraft configurations can otherwise benefit from their use, but it has not been generally established that winglets are preferable to or more efficient than simple wing span extensions to reduce induced drag. In many cases the relative benefit of winglets is marginal or even cosmetic.
The basic theory behind conventional tip devices on wings and foils is to block the flow of high pressure air from the lower surface to the upper surface at the unbounded termination point (wingtip). Blocking the flow helps reduce vortex formation and decreases the negative effects of the wingtip. Many concepts have been proposed to block the flow of fluid from the high pressure surface to the low pressure surface. The physical manifestations of these concepts are generally termed winglets, wing strakes, end plates, or other similar structures attached to the unbounded end of the wing or foil. Theoretically, if a winglet blocked all the flow from the high to the low pressure at the end of the wing or foil, the wing or foil would approach the efficiency of a two dimensional airfoil of infinite length. The conventional structures mentioned above are somewhat effective and do reduce the flow of fluid from the high pressure side to the low pressure side of the wing or foil, but they do not block all the flow and they do not prevent the formation of a vortex at the termination point, e.g, a wingtip vortex. Therefore, a need remains for improved methods and devices for handling such a vortex and the resulting lift-induced drag.